Historically, the average waiting time spent in a queue on Friday afternoon at a bank's city branch was 10 minutes. To determine whether their new multi-queuing system constitutes an improvement, a random sample of 15 customers was taken and their waiting time recorded. The results are in the X1 column of the data file P14.12 which can be found in a folder under the CML Quizzes tab. Assume the distribution of waiting times is normally distributed.
1. State the direction of the alternative hypothesis used to test whether there is an improvement in average waiting time. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as required in the box.
2. Calculate the test statistic correct to three decimal places (hint: use Descriptive Statistics to calculated the standard deviation and sample mean).
3. Use Kaddstat to determine the p-value for the test correct to four decimal places.
4. Is the null hypothesis rejected for this test if a 5% level of significance is used? Type yes or no.
5. Regardless of your answer for 4, if the null hypothesis was rejected, can we conclude that the average waiting time has improved with the new queuing system? Type yes or no.
Y X1 X2
28 12.6 134
43 11.4 126
45 11.5 143
49 11.1 152
57 10.4 143
68 9.6 147
74 9.8 128
81 8.4 119
82 8.8 130
86 8.9 135
101 8.1 141
112 7.6 123
114 7.8 121
119 7.4 129
124 6.4 135